Geodesic
A~Markov model for the dynamics of cracks of a~special type
Sibirskij žurnal industrialʹnoj matematiki, Tome 21 (2018) no. 1, pp. 72-79.

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Stochastic Markov models describe various natural and technical processes. They are often used in the most diverse fields. We single out the Markov models with discrete time and small number of states. In specific cases, such models allow carrying out effective analysis and calculations. We discuss in detail the models with four states. The processes associated with the elliptic cracks are simulated.
Keywords: stochastic modeling, Markov model, probability, dynamics, crack. 
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     title = {A~Markov model for the dynamics of cracks of a~special type},
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L. Ya. Savel'ev. A~Markov model for the dynamics of cracks of a~special type. Sibirskij žurnal industrialʹnoj matematiki, Tome 21 (2018) no. 1, pp. 72-79. http://geodesic.mathdoc.fr/item/SJIM_2018_21_1_a6/

[1] Kemeni Dzh., Snell Dzh., Konechnye tsepi Markova, Nauka, M., 1970 | MR

[2] Romanovskii V. I., Diskretnye tsepi Markova, Gostekhizdat, M., 1949 | MR

[3] Savelev L., Balakin S., Konechnye markovskie tsepi i serii (teoriya i prilozheniya), Lambert Acad. Publ., Saabrücken, 2012

[4] Savelev L. Ya., “Prostye stokhasticheskie modeli treschin”, Sib. zhurn. industr. matematiki, 17:2(58) (2014), 97–106 | MR

[5] Tikhomirov V. M., Surovin P. G., “Razvitie ustalostnykh treschin smeshannogo tipa v obraztsakh iz stali”, Prikl. mekhanika i tekhn. fizika, 45:1 (2004), 135–142

[6] Yunping X., Zdeniik P., “Random grown of crack with $R$-curve: Markov process model”, Engrg. Fracture Mech., 57:6 (1997), 593–608 | DOI